Norm inequalities for the iterated perturbations of Laplace transformers generated by accretive $$\scriptstyle N$$-tuples of operators in Q and Q* ideals of compact operators

Jocić, Danko R.; Golubović, Zora Lj.; Krstić, Mihailo; Milašinović, Stevan

doi:10.1007/s43034-024-00364-7

Ann. Funct. Anal.

2024

DOI: 10.1007/s43034-024-00364-7

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Norm inequalities for the iterated perturbations of Laplace transformers generated by accretive $$\scriptstyle N$$-tuples of operators in Q and Q* ideals of compact operators

Danko R. Jocić,

Zora Lj. Golubović,

Mihailo Krstić

et al.

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Norm Estimates for Remainders of Noncommutative Taylor Approximations for Laplace Transformers Defined by Hyperaccretive Operators

Jocić

2024

Mathematics

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Let H be a separable complex Hilbert space, B(H) the algebra of bounded linear operators on H, μ a finite Borel measure on R+ with the finite (n+1)-th moment, f(z):=∫R+e−tzdμ(t) for all ℜz⩾0,CΨ(H), and ||·||Ψ the ideal of compact operators and the norm associated to a symmetrically norming function Ψ, respectively. If A,D∈B(H) are accretive, then the Laplace transformer on B(H),X↦∫R+e−tAXe−tDdμ(t) is well defined for any X∈B(H) as is the newly introduced Taylor remainder transformer Rn(f;D,A)X:=f(A)X−∑k=0n1k!∑i=0k(−1)ikiAk−iXDif(k)(D). If A,D* are also (n+1)-accretive, ∑k=0n+1(−1)kn+1kAn+1−kXDk∈CΨ(H) and ||·||Ψ is Q* norm, then ||·||Ψ norm estimates for ∑k=0n+1n+1kAkAn+1−k12Rn(f;D,A)X∑k=0n+1n+1kDn+1−kD*k12 are obtained as the spacial cases of the presented estimates for (also newly introduced) Taylor remainder transformers related to a pair of Laplace transformers, defined by a subclass of accretive operators.

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Norm Estimates for Remainders of Noncommutative Taylor Approximations for Laplace Transformers Defined by Hyperaccretive Operators

Jocić

2024

Mathematics

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Norm inequalities for the iterated perturbations of Laplace transformers generated by accretive $$\scriptstyle N$$-tuples of operators in Q and Q* ideals of compact operators

Cited by 1 publication

References 13 publications

Norm Estimates for Remainders of Noncommutative Taylor Approximations for Laplace Transformers Defined by Hyperaccretive Operators

Norm Estimates for Remainders of Noncommutative Taylor Approximations for Laplace Transformers Defined by Hyperaccretive Operators

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